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<MODELING>
< ELECTRIC CIRCUITS >
< PRESENTATION >
< DAWOOD AHMED >
< REG# 194 >
< 24TH DECEMBER >
ELECTRIC CIRCUITS:
An electronic circuit is composed of
individual electronic components,
such as resistors, transistors,
capacitors, inductors and diodes,
connected by conductive wires or
traces through which electric current
MODELING:
• A mathematical model is a description of
a system using mathematical concepts and language.
• The process of developing a mathematical model is
termed mathematical modeling. Mathematical models are used in
the natural sciences (such as physics, biology, earth
science, chemistry) and engineering disciplines (such as computer
science, electrical engineering), as well as in non-physical systems
such as the social sciences (such
as economics, psychology, sociology, political science).
• Mathematical models are also used in music, linguistics
and philosophy (for example, intensively in analytic philosophy).
MODELING:
•A model may help to explain a system and
to study the effects of different
components, and to make predictions
about behavior.
ELEMENTS IN AN RLC-CIRCUIT:
RESISTOR:
•In bellow the circuit model of resistor is shown
in Fig.
•The mathematical model is given by the
Ohm’s law relationship,
INDUCTOR:
•In bellow the the circuit representation is
shown in Fig.
•The input output relations are given by
Faraday’s law,
SELF-INDUCTANCE:
• If only a single coil is considered, the inductance is
known as self-inductance. If a voltage is induced in a
as second coil due to a current in the first coil, the
voltage is said to be due to mutual inductance, as
shown in Fig
CAPACITOR:
•In bellow the circuit symbol of a capacitor
is given in Fig.
•If we integration of v(t) is known as the
charge on the capacitor and is denoted
by ‘q’. Thus
FIGURE 1:
FIGURE 1 EXPLANATION:
•Figure 1 shows an RLC-circuit, as it occurs
as a basic building block of large electric
networks in computers and elsewhere. An
RLC-circuit is obtained from an RL-circuit
by adding a capacitor.
ANALOGY OF ELECTRICAL AND
MECHANICAL QUANTITIES:
• Entirely different physical or other systems may have
the same mathematical model.
• This analogy is strictly quantitative in the sense that to
a given mechanical system.
• we can construct an electric circuit whose current will
give the exact values of the displacement in the
mechanical system when suitable scale factors are
introduced.
• The practical importance of this analogy is almost
obvious. The analogy may be used for constructing an
“electrical model” of a given mechanical model,
•In above discussion we can see the
Mathematical Modelling of Electrical Systems
which has come to act when we go for Laplace
transform. It will come to act when we will go
for calculate transient response of an electrical
systems in time domain.
•Hope this above discussion on Mathematical
Modelling of Electrical Systems will be
helpful to you.
Q A
hank You

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Mathematical Modeling of electric circuit

  • 2. < PRESENTATION > < DAWOOD AHMED > < REG# 194 > < 24TH DECEMBER >
  • 3. ELECTRIC CIRCUITS: An electronic circuit is composed of individual electronic components, such as resistors, transistors, capacitors, inductors and diodes, connected by conductive wires or traces through which electric current
  • 4. MODELING: • A mathematical model is a description of a system using mathematical concepts and language. • The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science). • Mathematical models are also used in music, linguistics and philosophy (for example, intensively in analytic philosophy).
  • 5. MODELING: •A model may help to explain a system and to study the effects of different components, and to make predictions about behavior.
  • 6. ELEMENTS IN AN RLC-CIRCUIT:
  • 7. RESISTOR: •In bellow the circuit model of resistor is shown in Fig. •The mathematical model is given by the Ohm’s law relationship,
  • 8. INDUCTOR: •In bellow the the circuit representation is shown in Fig. •The input output relations are given by Faraday’s law,
  • 9.
  • 10. SELF-INDUCTANCE: • If only a single coil is considered, the inductance is known as self-inductance. If a voltage is induced in a as second coil due to a current in the first coil, the voltage is said to be due to mutual inductance, as shown in Fig
  • 11. CAPACITOR: •In bellow the circuit symbol of a capacitor is given in Fig. •If we integration of v(t) is known as the charge on the capacitor and is denoted by ‘q’. Thus
  • 13. FIGURE 1 EXPLANATION: •Figure 1 shows an RLC-circuit, as it occurs as a basic building block of large electric networks in computers and elsewhere. An RLC-circuit is obtained from an RL-circuit by adding a capacitor.
  • 14. ANALOGY OF ELECTRICAL AND MECHANICAL QUANTITIES: • Entirely different physical or other systems may have the same mathematical model. • This analogy is strictly quantitative in the sense that to a given mechanical system. • we can construct an electric circuit whose current will give the exact values of the displacement in the mechanical system when suitable scale factors are introduced.
  • 15. • The practical importance of this analogy is almost obvious. The analogy may be used for constructing an “electrical model” of a given mechanical model,
  • 16. •In above discussion we can see the Mathematical Modelling of Electrical Systems which has come to act when we go for Laplace transform. It will come to act when we will go for calculate transient response of an electrical systems in time domain. •Hope this above discussion on Mathematical Modelling of Electrical Systems will be helpful to you.
  • 17. Q A